**3.1. Introduction**

382 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications

implemented MIMO-systems can be found in chapter 11 *ultraMedis*.

**Figure 6.** Creation of a MIMO-system by cascading M-sequence sensors.

the opposite will happen.

measurements. This favors the PN-sensor concept for applications dealing with super resolution techniques or micro-Doppler problems, particularly if weak scattering targets are overwhelmed by strong ones. Chapter11 *ultraMedis* gives some examples of related problems, and Fig. 5 illustrates the achieved short-time stability of an M-sequence sensor having a bandwidth of about 8 GHz. The short-time variance of the pulse position measurement was in the lower fs range corresponding to a distance variation below 1 µm.

The simple timing concept of the PN-sensors enables the implementation of large MIMOarrays at which the number of cascaded measurement units is basically not limited. The principle is shown in Fig. 6. However, the data handling will be increasingly demanding with a rising number of channels. In a typical operation mode, the transmitters are sequentially activated while the receivers of all channels work in parallel. Some details of

The receiver of the UWB PN-sensor applies sub-sampling for data capture. Hence, its efficiency gives some potential of further improvements. This would, however, be connected with a considerable increase of the sampling rate *sf* . As we can see from (8), the elevation of the sampling rate has to be done at the expense of the ADC resolution since the FoM-value is primarily fixed by the semi-conductor technology, while the maximum power is limited by the achievable heat transport. However, simply increasing the sampling rate based on low bit ADCs will not bring any profit with respect to the sensor performance, i.e.

As, however, the update rate of UWB PN-sensors is much higher than required by the time variance of the test object, the difference between two consecutive measurements is very low so that low resolution ADCs are sufficient for capturing these deviations. Anyway, this supposes a fast control loop and a (less power hungry) DAC of sufficient resolution which provides the captured signals from previous measurements for reference. Some basic considerations related to this type of feedback sampling can be found in [2]. Details of the layout and implementation of related sub-components are discussed in sections 3.4, 5 and 6.2.

In order to support system design in its individual stages, different amplifier versions have been developed. Classical ultra-wideband low-noise amplifiers (UWB-LNAs) have been implemented first to ensure early availability and to assess the SiGe BiCMOS technology applied. Then, new receiving components have been considered to address the requirements discovered in system design. This way, a new subtraction amplifier has been made available which allows for practical evaluation of the feedback sampling approach. **Fig. 7** illustrates the way in which LNAs and subtraction amplifiers are used as part of the system.

**Figure 7.** Transmit and receive path of the basic UWB PN-device from Fig. 4 (solid lines) and proposed extension to allow for feedback sampling (dashed lines – see subsection 6.2.3). Either the LNA component or the amplifier with integrated signal subtraction capability are present (dash-dotted box) according to the system state at which it is focused.

In this figure, the basic M-Sequence system is indicated by solid lines. Within this system, classical UWB-LNAs (the LNA component in the dash-dotted box) are used to support the way of operation presented in subsection 2.3. Possible implementations are covered in subsections 3.2.1 to 3.2.3. In addition, a system extension is indicated by the dashed lines, which tries to overcome the limitations imposed by the analog-to-digital converter. For this reason, a digitally calculated prediction signal is provided by a digital-to-analog converter and subtracted from the receive signal to generate a difference signal of highly reduced signal swing close to sampling time instances (see sections 5.1 and 6.2.3). Subtraction is performed by an amplifier with integrated signal subtraction capability, practical realizations of which are presented in sections 3.4.1 and 3.4.2.

The latest subtractor also accounts for low feeding point impedance, which is imperative for the conceptual design of dielectrically scaled antennas. The use of such a device is intended by the collaborative project *ultraMedis* (see chapter 11). For establishing common interface definitions, the performance of individual components has to be characterized by appropriate metrics. While those are well established for single-ended arrangements, this is not the case with the noise characterization of multiport or differential structures. Hence, a new de-embedding scheme for the noise figure of a differential device has been developed and will be presented.

HaLoS – Integrated RF-Hardware Components for Ultra-Wideband Localization and Sensing 385

of the second stage, is treated as single compound-transistor *Q*<sup>23</sup> . Within the simplified circuit thus obtained, four feedback loops can be identified. For proper biasing, series-series feedback is applied to *Q*1 and *Q*<sup>23</sup> . By this measure, the bandwidth of both stages is improved. In turn, input and output impedances of the amplifier are increased rather than

 **Figure 8.** Schematic diagram (left) and chip photo (right) of the multiple resistive feedback LNA - the

*RM1*

*Q4*

*RM2*

Hence, local shunt-shunt feedback is applied to *Q*23 in order to reduce the output impedance. Finally, to enable input power matching, global shunt-series feedback from the emitter node of *Q*23 to the base of *Q*1 is applied. According to [10], this configuration tends to present an overdamped response. For this reason, peaking capacitors *CP*1 and *CP*2 are inserted to improve the frequency behavior of the amplifier. The addition of peaking capacitors might, however, impair stability which has to be diligently observed during design for this reason as stated in [13]. In the same publication, an approximate calculation of the noise figure (NF) for this topology reveals that the latter is dominated by the noise properties of *Q*1 as long as *R R <sup>F</sup>*<sup>1</sup> *<sup>S</sup>* and *R R <sup>F</sup>*<sup>1</sup> *eq* . *Req* is related to the equivalent input

transistor *Q*<sup>1</sup> 's bias current to yield optimal current density with respect to its noise properties should be a first step in design. After this initial step, one of the directed design procedures given in [10] or [9], respectively, can be used for further development. Those are derived from input and output power match conditions as well as from pole positions. In order to account for the characteristics of the Darlington pair transistors *Q*2 and *Q*<sup>3</sup> ,

an emitter follower has been attached for further improving the output power matching in the technology used. Fig. 8 (right) shows the chip photograph of the implemented LNA without pads used for biasing. The dimensions of the displayed die area are 530 280

only, which confirms the advantage resistive feedback amplifiers provide in view of die area as compared to resonant solutions. For the accurate characterization of the fabricated

<sup>1</sup> / (4 ) *R v kT eq Q* . For this reason, the selection of

can be applied according to [10]. In Fig. 8 (left),

*m m* 

decreased as required for input and output power matching.

*Q3*

*VCC VCC VCC*

*RL1 RL2*

*CC CC*

*RD1 RD2 vin vout*

*Q2*

*CP1 CP2*

*RE1 RE2*

die area is only 530 µm × 280 µm.

*Q1*

*RF1*

*RF2*

noise voltage source *<sup>Q</sup>*<sup>1</sup> *v* of transistor *Q*1 by <sup>2</sup>

*T T* 

substitutions *m m* ,23 ,3 *g g* and ,23 ,3 2

### **3.2. LNAs for the basic M-Sequence system**

Within the basic M-sequence system, low noise amplifiers (LNAs) perform the classical task of adapting the input signal swing to the dynamic range of the analog-to-digital converter (ADC) while adding only a minimum amount of excess noise and providing reasonable power-match conditions. If a high-gain LNA is used, the system also is less sensitive to noise added by succeeding components. Gain, in turn, is limited by the required linearity, and an appropriate compromise with respect to all counteracting requirements has to be found. While trading one parameter against the other, the conditions set by the technology have to be considered for the individual LNA. Resonant tuning and resistive feedback topologies are predominantly used in literature for mapping specifications to circuit designs. Though a resonant solution is favored in [11], the authors do admit that the parasitic base resistance of bipolar transistors causes a large contribution to output noise. Thus, the advantage of extraordinary low noise figures enabled by narrow-band resonant designs as compared to designs matched by resistive feedback is relativized. High magnetic field gradients potentially encountered in some of the applications, and the limited ability to use shielding as identified in [12] also make the use of inductors questionable. Therefore, resistive feedback solutions have been preferred as their use is additionally accompanied by notable die size advantages. While the design of individual amplifiers will be covered in the following subsections, general guidelines can be taken from standard textbooks. In [13], for example, the impact of feedback on noise and impedance match is analyzed in detail. For the design, too, a simplified version of the bipolar transistor small signal equivalent circuit model with additional noise sources as presented in [13] has been used.

### *3.2.1. Multiple resistive feedback LNA*

One of the implemented amplifier versions which have been inspired by classical UWB-LNAs is depicted in Fig. 8. According to [10], this is a popular wideband amplifier topology often referred to as *Kukielka* amplifier. Due to numerous results reported in literature for this kind of amplifier, the impact of technology on circuit performance can be assessed. For comparison, especially SiGe implementations as presented in [9] are valuable. The main characteristics of this amplifier are set by the core circuit which comprises transistors *Q*<sup>1</sup> to *Q*<sup>3</sup> . For analysis, the Darlington pair *Q Q* 2 3 , which is used for gain-bandwidth extension of the second stage, is treated as single compound-transistor *Q*<sup>23</sup> . Within the simplified circuit thus obtained, four feedback loops can be identified. For proper biasing, series-series feedback is applied to *Q*1 and *Q*<sup>23</sup> . By this measure, the bandwidth of both stages is improved. In turn, input and output impedances of the amplifier are increased rather than decreased as required for input and output power matching.

384 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications

model with additional noise sources as presented in [13] has been used.

One of the implemented amplifier versions which have been inspired by classical UWB-LNAs is depicted in Fig. 8. According to [10], this is a popular wideband amplifier topology often referred to as *Kukielka* amplifier. Due to numerous results reported in literature for this kind of amplifier, the impact of technology on circuit performance can be assessed. For comparison, especially SiGe implementations as presented in [9] are valuable. The main characteristics of this amplifier are set by the core circuit which comprises transistors *Q*<sup>1</sup> to *Q*<sup>3</sup> . For analysis, the Darlington pair *Q Q* 2 3 , which is used for gain-bandwidth extension

*3.2.1. Multiple resistive feedback LNA* 

and will be presented.

**3.2. LNAs for the basic M-Sequence system** 

The latest subtractor also accounts for low feeding point impedance, which is imperative for the conceptual design of dielectrically scaled antennas. The use of such a device is intended by the collaborative project *ultraMedis* (see chapter 11). For establishing common interface definitions, the performance of individual components has to be characterized by appropriate metrics. While those are well established for single-ended arrangements, this is not the case with the noise characterization of multiport or differential structures. Hence, a new de-embedding scheme for the noise figure of a differential device has been developed

Within the basic M-sequence system, low noise amplifiers (LNAs) perform the classical task of adapting the input signal swing to the dynamic range of the analog-to-digital converter (ADC) while adding only a minimum amount of excess noise and providing reasonable power-match conditions. If a high-gain LNA is used, the system also is less sensitive to noise added by succeeding components. Gain, in turn, is limited by the required linearity, and an appropriate compromise with respect to all counteracting requirements has to be found. While trading one parameter against the other, the conditions set by the technology have to be considered for the individual LNA. Resonant tuning and resistive feedback topologies are predominantly used in literature for mapping specifications to circuit designs. Though a resonant solution is favored in [11], the authors do admit that the parasitic base resistance of bipolar transistors causes a large contribution to output noise. Thus, the advantage of extraordinary low noise figures enabled by narrow-band resonant designs as compared to designs matched by resistive feedback is relativized. High magnetic field gradients potentially encountered in some of the applications, and the limited ability to use shielding as identified in [12] also make the use of inductors questionable. Therefore, resistive feedback solutions have been preferred as their use is additionally accompanied by notable die size advantages. While the design of individual amplifiers will be covered in the following subsections, general guidelines can be taken from standard textbooks. In [13], for example, the impact of feedback on noise and impedance match is analyzed in detail. For the design, too, a simplified version of the bipolar transistor small signal equivalent circuit

**Figure 8.** Schematic diagram (left) and chip photo (right) of the multiple resistive feedback LNA - the die area is only 530 µm × 280 µm.

Hence, local shunt-shunt feedback is applied to *Q*23 in order to reduce the output impedance. Finally, to enable input power matching, global shunt-series feedback from the emitter node of *Q*23 to the base of *Q*1 is applied. According to [10], this configuration tends to present an overdamped response. For this reason, peaking capacitors *CP*1 and *CP*2 are inserted to improve the frequency behavior of the amplifier. The addition of peaking capacitors might, however, impair stability which has to be diligently observed during design for this reason as stated in [13]. In the same publication, an approximate calculation of the noise figure (NF) for this topology reveals that the latter is dominated by the noise properties of *Q*1 as long as *R R <sup>F</sup>*<sup>1</sup> *<sup>S</sup>* and *R R <sup>F</sup>*<sup>1</sup> *eq* . *Req* is related to the equivalent input noise voltage source *<sup>Q</sup>*<sup>1</sup> *v* of transistor *Q*1 by <sup>2</sup> <sup>1</sup> / (4 ) *R v kT eq Q* . For this reason, the selection of transistor *Q*<sup>1</sup> 's bias current to yield optimal current density with respect to its noise properties should be a first step in design. After this initial step, one of the directed design procedures given in [10] or [9], respectively, can be used for further development. Those are derived from input and output power match conditions as well as from pole positions. In order to account for the characteristics of the Darlington pair transistors *Q*2 and *Q*<sup>3</sup> , substitutions *m m* ,23 ,3 *g g* and ,23 ,3 2 *T T* can be applied according to [10]. In Fig. 8 (left), an emitter follower has been attached for further improving the output power matching in the technology used. Fig. 8 (right) shows the chip photograph of the implemented LNA without pads used for biasing. The dimensions of the displayed die area are 530 280 *m m* only, which confirms the advantage resistive feedback amplifiers provide in view of die area as compared to resonant solutions. For the accurate characterization of the fabricated amplifier, on-waver measurements have been performed using a PM 8 probe station of Süss MicroTec (now acquired by Cascade Microtech). Due to the measurement arrangement, losses preceding and succeeding the device under test (DUT), i.e. the amplifier, cannot be avoided. However, their impact on the scattering parameters of the DUT can be eliminated by proper calibration of the network analyzer applied. Also, the spectrum analyzer with noise figure measurement personality in use allows for the specification of losses preceding and succeeding the DUT which are compensated for during measurement in this case2. Measurement results obtained in this way are shown in Fig. 9 together with results from post-layout simulation. Initially, they have been presented in [14].

HaLoS – Integrated RF-Hardware Components for Ultra-Wideband Localization and Sensing 387

 **Figure 10.** Schematic diagram (left) and chip photo of both active feedback LNA versions (right). The

It is a one-stage amplifier with resistive emitter degeneration to ensure a stable DC operating point and to improve bandwidth. Due to the presence of the peaking capacitor *CP* , degeneration is continuously shifted to higher frequencies. As in the case of the multiple resistive feedback amplifier, this technique has to be used with care to ensure that this measure does not impair amplifier stability. Input matching of *Q*1 is achieved by feedback via transistor *Q*2 as well as resistors *RF*1 and *RF* <sup>2</sup> . The advantage of *Q*2 is twofold: It improves the isolation between the input node and the output node in forward direction and, according to [15], it helps to enlarge the collector-emitter voltage of *Q*<sup>1</sup> . Thus, the maximum oscillation frequency *max f* is expected to be increased, and the large-signal behavior is said to be improved. The amplifier according to Fig. 10 was presented in [14] for the first time. Compared to the amplifier in [15], the inductor used for improving the frequency behavior has been abscised from the design while the peaking capacitor has been added. Also, for better output matching, emitter follower *Q*3 has been attached. To avoid a lengthy discussion of circuit characteristics, Fig. 10 (left) uses an alternative way to depict the circuit as compared to [14] or [15]. This representation points out the large similarity of feedback paths in both amplifiers shown in Fig. 8 and Fig. 10. Though the actual implementations of the passive feedback networks differ, shunt-series feedback is applied for input matching in both cases, and many design steps can be executed by analogy. Fig. 10 (right) shows the chip photograph of two variants, which have been implemented to assess the impact of layout on circuit performance. In the first version, 90° lead corners are avoided and consecutive 45° lead corners are used instead. By this measure, the average lead length is increased. By contrast, a compact design has been targeted in the second layout version. As discussed in [14], results do not differ significantly as long as the length of the lead connecting the RF input with the first amplifying transistor is kept comparably long. Thus,

 *m m* , respectively.

*vout CC*

die areas are (1) 630 280

*vin*

*CC*

*RF2 RE CP*

R*F1 Q1*

> 

*VCC VCC VCC*

Q2 Q3

RM1

RM2

*m m* and (2) 530 280

only results for the second layout version are shown in Fig. 11.

**Figure 9.** Measurement results of the multiple resistive feedback LNA. (The arrows point to the related axis scaling.)

From Fig. 9, peaking in the gain curve progression of the measurement data can be observed as compared to the results from post layout simulation. The maximum difference appears at about 8 GHz, which is the frequency at which a notch in measured 11 *S* values also appears. In [14] it is thus suspected that this deviation arises due to the interaction of the test set-up with the DUT. In short summary, the results presented in Fig. 9 for the low-cost technology applied map pretty well the state-of-the-art performances reported in literature at that time. For a more detailed analysis, the reader may consult [14].

### *3.2.2. Active Feedback LNA*

This amplifier has been inspired by the work presented in [15]. Due to the characteristics of the applied technology, certain adaptations have been required, though. Fig. 10 (left) shows the schematic diagram of the final design.

<sup>2</sup> Rhode & Schwarz ZVA-24 and FSQ-40 have been used for the measurements.

386 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications

post-layout simulation. Initially, they have been presented in [14].

For a more detailed analysis, the reader may consult [14].

2 Rhode & Schwarz ZVA-24 and FSQ-40 have been used for the measurements.

axis scaling.)

*3.2.2. Active Feedback LNA* 

the schematic diagram of the final design.

amplifier, on-waver measurements have been performed using a PM 8 probe station of Süss MicroTec (now acquired by Cascade Microtech). Due to the measurement arrangement, losses preceding and succeeding the device under test (DUT), i.e. the amplifier, cannot be avoided. However, their impact on the scattering parameters of the DUT can be eliminated by proper calibration of the network analyzer applied. Also, the spectrum analyzer with noise figure measurement personality in use allows for the specification of losses preceding and succeeding the DUT which are compensated for during measurement in this case2. Measurement results obtained in this way are shown in Fig. 9 together with results from

**Figure 9.** Measurement results of the multiple resistive feedback LNA. (The arrows point to the related

From Fig. 9, peaking in the gain curve progression of the measurement data can be observed as compared to the results from post layout simulation. The maximum difference appears at about 8 GHz, which is the frequency at which a notch in measured 11 *S* values also appears. In [14] it is thus suspected that this deviation arises due to the interaction of the test set-up with the DUT. In short summary, the results presented in Fig. 9 for the low-cost technology applied map pretty well the state-of-the-art performances reported in literature at that time.

This amplifier has been inspired by the work presented in [15]. Due to the characteristics of the applied technology, certain adaptations have been required, though. Fig. 10 (left) shows

**Figure 10.** Schematic diagram (left) and chip photo of both active feedback LNA versions (right). The die areas are (1) 630 280 *m m* and (2) 530 280 *m m* , respectively.

It is a one-stage amplifier with resistive emitter degeneration to ensure a stable DC operating point and to improve bandwidth. Due to the presence of the peaking capacitor *CP* , degeneration is continuously shifted to higher frequencies. As in the case of the multiple resistive feedback amplifier, this technique has to be used with care to ensure that this measure does not impair amplifier stability. Input matching of *Q*1 is achieved by feedback via transistor *Q*2 as well as resistors *RF*1 and *RF* <sup>2</sup> . The advantage of *Q*2 is twofold: It improves the isolation between the input node and the output node in forward direction and, according to [15], it helps to enlarge the collector-emitter voltage of *Q*<sup>1</sup> . Thus, the maximum oscillation frequency *max f* is expected to be increased, and the large-signal behavior is said to be improved. The amplifier according to Fig. 10 was presented in [14] for the first time. Compared to the amplifier in [15], the inductor used for improving the frequency behavior has been abscised from the design while the peaking capacitor has been added. Also, for better output matching, emitter follower *Q*3 has been attached. To avoid a lengthy discussion of circuit characteristics, Fig. 10 (left) uses an alternative way to depict the circuit as compared to [14] or [15]. This representation points out the large similarity of feedback paths in both amplifiers shown in Fig. 8 and Fig. 10. Though the actual implementations of the passive feedback networks differ, shunt-series feedback is applied for input matching in both cases, and many design steps can be executed by analogy. Fig. 10 (right) shows the chip photograph of two variants, which have been implemented to assess the impact of layout on circuit performance. In the first version, 90° lead corners are avoided and consecutive 45° lead corners are used instead. By this measure, the average lead length is increased. By contrast, a compact design has been targeted in the second layout version. As discussed in [14], results do not differ significantly as long as the length of the lead connecting the RF input with the first amplifying transistor is kept comparably long. Thus, only results for the second layout version are shown in Fig. 11.

HaLoS – Integrated RF-Hardware Components for Ultra-Wideband Localization and Sensing 389

aspects, they are discussed in [18] in more detail. Measurements to gather those results have been performed on-waver at the PM 8 probe station using ground-signal-signal-ground (GSSG) probes. Similar to the single-ended case, scattering parameters could be determined directly by a calibrated network analyzer. By contrast, only single-ended equipment has been available for noise figure measurement, and it is left to the next subsection to discuss a

**Figure 12.** Half-circuit schematic diagram (left) and chip photo (right) of the pseudo-differential LNA.

**Figure 13.** Measurement results of the pseudo-differential LNA. (The arrows point to the related axis

Due to space limitations, only a short introduction to this topic will be presented here. While there are alternative methods as presented in [23] and [24], for example, focus will be on a

scaling.)

**3.3. Differential noise figure measurement** 

method applicable to (pseudo-)differential amplifiers.

**Figure 11.** Measurement results of the active feedback LNA. (The arrows point to the related axis scaling.)

The die area occupied by the first layout version is 630μ*m m* 280 while the second layout version only occupies 530 280 *m m* (both excluding DC-pads). Measurements have been performed the same way as explained for the multiple resistive feedback LNA. Compared to Fig. 9, gain is much lower, which is expected due to the single stage nature of the active feedback amplifier. At the same time, the input referred 1 *dB* compression point is improved notably. A more complete discussion of amplifier characteristics is presented in [14].

### *3.2.3. Pseudo-differential LNA*

Core of the half-circuit shown in Fig. 12 (left) is the cascode amplifier with reactive shunt feedback on the left-hand side. As for the single-ended amplifiers, bias current of this arrangement should be selected due to noise and linearity considerations. While a more detailed analysis of this topology, as presented for the inductively degenerated cascade amplifier with capacitive shunt feedback in [16], might be desirable at this point, limited space for this section does not permit a lengthy discussion. Instead, we allude to the amplifier of [17] from which the topology of Fig. 12 (left) has been derived.

A pseudo-differential amplifier has been implemented to support the development of the basic M-sequence system by adding the capability to use differential circuitry, especially differential antennas. Many of its characteristics are inherited from the topology of [17]. However, emphasis with respect to certain design parameters has been shifted. The most peculiar aspect is the fact that the input matching network used in [17] could be abscised from the design. This modification was enabled by improved input-output isolation due to altered feedback tapping points. Some results of the manufactured chip, a photo of which is contained in Fig. 12 (right), are summarized in Fig. 13. Together with additional topological aspects, they are discussed in [18] in more detail. Measurements to gather those results have been performed on-waver at the PM 8 probe station using ground-signal-signal-ground (GSSG) probes. Similar to the single-ended case, scattering parameters could be determined directly by a calibrated network analyzer. By contrast, only single-ended equipment has been available for noise figure measurement, and it is left to the next subsection to discuss a method applicable to (pseudo-)differential amplifiers.

388 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications

**Figure 11.** Measurement results of the active feedback LNA. (The arrows point to the related axis

notably. A more complete discussion of amplifier characteristics is presented in [14].

amplifier of [17] from which the topology of Fig. 12 (left) has been derived.

performed the same way as explained for the multiple resistive feedback LNA. Compared to Fig. 9, gain is much lower, which is expected due to the single stage nature of the active feedback amplifier. At the same time, the input referred 1 *dB* compression point is improved

Core of the half-circuit shown in Fig. 12 (left) is the cascode amplifier with reactive shunt feedback on the left-hand side. As for the single-ended amplifiers, bias current of this arrangement should be selected due to noise and linearity considerations. While a more detailed analysis of this topology, as presented for the inductively degenerated cascade amplifier with capacitive shunt feedback in [16], might be desirable at this point, limited space for this section does not permit a lengthy discussion. Instead, we allude to the

A pseudo-differential amplifier has been implemented to support the development of the basic M-sequence system by adding the capability to use differential circuitry, especially differential antennas. Many of its characteristics are inherited from the topology of [17]. However, emphasis with respect to certain design parameters has been shifted. The most peculiar aspect is the fact that the input matching network used in [17] could be abscised from the design. This modification was enabled by improved input-output isolation due to altered feedback tapping points. Some results of the manufactured chip, a photo of which is contained in Fig. 12 (right), are summarized in Fig. 13. Together with additional topological

(both excluding DC-pads). Measurements have been

while the second layout

The die area occupied by the first layout version is 630μ*m m* 280

*m m* 

scaling.)

version only occupies 530 280

*3.2.3. Pseudo-differential LNA* 

**Figure 12.** Half-circuit schematic diagram (left) and chip photo (right) of the pseudo-differential LNA.

**Figure 13.** Measurement results of the pseudo-differential LNA. (The arrows point to the related axis scaling.)

### **3.3. Differential noise figure measurement**

Due to space limitations, only a short introduction to this topic will be presented here. While there are alternative methods as presented in [23] and [24], for example, focus will be on a

### 390 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications

new powerful method proposed in [20]. A convenient definition for the noise figure of a differential (or multiport) device with respect to one of its ports has been given by Randa [22] and is reprinted in (11) with slight modifications:

$$F\_i\left(\Gamma\_k, \mathbf{C}\_k\right) = \frac{\left\{ \left[\mathbf{I} - \mathbf{S}\_k \Gamma\_k\right]^{-1} \left(\mathbf{S}\_k \mathbf{C}\_k \mathbf{S}\_k^\dagger + \mathbf{C}\_{S,a}\right) \left[\left[\mathbf{I} - \mathbf{S}\_k \Gamma\_k\right]^{-1}\right]^\dagger \right\}\_{ii}}{\left\{ \left[\mathbf{I} - \mathbf{S}\_k \Gamma\_k\right]^{-1} \mathbf{S}\_k \mathbf{C}\_k \mathbf{S}\_k^\dagger \left[\left[\mathbf{I} - \mathbf{S}\_k \Gamma\_k\right]^{-1}\right]^\dagger \right\}\_{ii}} \tag{11}$$

HaLoS – Integrated RF-Hardware Components for Ultra-Wideband Localization and Sensing 391

Making use of single-ended noise measurement equipment, the characteristic noise *equation* 

whole component chain, can also be determined. Thus, we are only left with the problem to describe signal transfer via the component chain to accomplish the goal of de-embedding **C***S a*, . In [20], an approach based on the connection scattering matrix **W** has been presented for this purpose, which surpassed the method of [19], because it is applicable without simplifying assumptions. The connection scattering matrix was introduced long ago, and its use for computer-aided circuit analysis has been discussed in [26], for example. For all ports in a component network, it relates the incident to the impressed waves. To enable such matrix representation, incident, reflected, and impressed waves have to be composed to wave vectors **a** , **b** , and *<sup>S</sup>* **b** , respectively, which should be sorted in a component-wise way. For convenience, a component index is assigned to the vector entries, and it is assumed that elements corresponding to the DUT (index *k* ) are placed at the bottom of each wave vector. An element is thus identified by two indices *i j*, representing the component and the respective port number. With this convention, all complex wave amplitudes can be related

where **S** is a block-diagonal matrix assembled from the individual component S-parameter matrices. The connections between the single components impose additional constraints on

Most often, a common real reference impedance is applied for all components. Then, all entries of **Γ** are zero except those which refer to connected ports and, thus, are one. In this case, **Γ** is a permutation matrix with 1 T **Γ Γ** . From (13) and (14) , the incident wave vector

Noise generated by the source does not contribute to the characteristic noise temperature of the component chain. The respective entries of *<sup>S</sup>* **b** can thus be set to zero. Furthermore, in the case of 1 **<sup>S</sup>** containing zero entries3, the corresponding rows of **<sup>W</sup>** <sup>1</sup> **<sup>Γ</sup>** should be deleted to avoid rank deficient matrix problems in some of the computations. For convenience, we will refer to the matrix obtained from this operation by **V** . After additional matrix

the wave amplitudes. To account for them, the connection matrix **Γ** is used as in (14):

*reference goes here*temperature ˆ

by the set of linear equations

**a** can be eliminated to get

<sup>1</sup> **S** is a submatrix of **S** .

 3

partitioning, which is required later, (15) then becomes

† † /( ) **N b b I SS** <sup>ˆ</sup> *S S kT* (12)

*chain T* , which characterizes noise from all the elements of the

*<sup>S</sup>* **b Sa b** (13)

**b Γa** (14)

1 , *<sup>S</sup> with* **<sup>W</sup><sup>Γ</sup> bb W <sup>Γ</sup> <sup>S</sup> <sup>W</sup> <sup>Γ</sup> S** (15)

The noise figure in (11) is parameterized by the matrix of reflection coefficients seen by the DUT into the ports of connected components **Γ***k* and the noise correlation matrix of incident noise waves injected by an external source **C***<sup>k</sup>* . **I** is the identity matrix in (11), the dagger indicates the Hermitian conjugate, and **S***k* as well as **C***S a*, are the scattering matrix and the noise correlation matrix of emergent waves contributed by the DUT, respectively. To apply this definition, **C***S a*, has to be determined first. Therefore, the differential device has to be embedded into a network of passive components which provide the differential excitation as only single-ended measurement equipment is currently available. This is demonstrated in Fig. 14. The noise correlation matrix of the DUT then has to be de-embedded from the results measured for the component chain.

**Figure 14.** DUT embedded into passive components. **b***Sx y*, are equivalent generator noise waves caused by component x and ejected from the respective port y.

For this purpose, the noise distribution matrix defined in [21] is a convenient starting point. Multiplied by Boltzmann's constant *k* and the physical temperature *T* , it is the correlation matrix of emergent noise waves caused by a passive component which account for all the noise generated within the device. It can be related to the scattering matrix as shown by (12). A short and intuitive proof of this relation is contained in [25]:

HaLoS – Integrated RF-Hardware Components for Ultra-Wideband Localization and Sensing 391

$$\hat{\mathbf{N}} = \left(\overline{\mathbf{b}\_{\text{S}} \mathbf{b}\_{\text{S}}^{\dagger}}\right) / (kT) = \mathbf{I} - \mathbf{S} \mathbf{S}^{\dagger} \tag{12}$$

Making use of single-ended noise measurement equipment, the characteristic noise *equation reference goes here*temperature ˆ *chain T* , which characterizes noise from all the elements of the whole component chain, can also be determined. Thus, we are only left with the problem to describe signal transfer via the component chain to accomplish the goal of de-embedding **C***S a*, . In [20], an approach based on the connection scattering matrix **W** has been presented for this purpose, which surpassed the method of [19], because it is applicable without simplifying assumptions. The connection scattering matrix was introduced long ago, and its use for computer-aided circuit analysis has been discussed in [26], for example. For all ports in a component network, it relates the incident to the impressed waves. To enable such matrix representation, incident, reflected, and impressed waves have to be composed to wave vectors **a** , **b** , and *<sup>S</sup>* **b** , respectively, which should be sorted in a component-wise way. For convenience, a component index is assigned to the vector entries, and it is assumed that elements corresponding to the DUT (index *k* ) are placed at the bottom of each wave vector. An element is thus identified by two indices *i j*, representing the component and the respective port number. With this convention, all complex wave amplitudes can be related by the set of linear equations

$$\mathbf{b} = \mathbf{S} \cdot \mathbf{a} + \mathbf{b}\_S \tag{13}$$

where **S** is a block-diagonal matrix assembled from the individual component S-parameter matrices. The connections between the single components impose additional constraints on the wave amplitudes. To account for them, the connection matrix **Γ** is used as in (14):

$$\mathbf{b} = \Gamma \cdot \mathbf{a} \tag{14}$$

Most often, a common real reference impedance is applied for all components. Then, all entries of **Γ** are zero except those which refer to connected ports and, thus, are one. In this case, **Γ** is a permutation matrix with 1 T **Γ Γ** . From (13) and (14) , the incident wave vector **a** can be eliminated to get

$$\mathbf{W}\,\Gamma^{-1}\mathbf{b} = \mathbf{b}\_{S'}\,\,\text{with}\,\,\mathbf{W} = \Gamma - \mathbf{S}\,\,\,\mathbf{W} = \Gamma - \mathbf{S}\tag{15}$$

Noise generated by the source does not contribute to the characteristic noise temperature of the component chain. The respective entries of *<sup>S</sup>* **b** can thus be set to zero. Furthermore, in the case of 1 **<sup>S</sup>** containing zero entries3, the corresponding rows of **<sup>W</sup>** <sup>1</sup> **<sup>Γ</sup>** should be deleted to avoid rank deficient matrix problems in some of the computations. For convenience, we will refer to the matrix obtained from this operation by **V** . After additional matrix partitioning, which is required later, (15) then becomes

390 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications

[22] and is reprinted in (11) with slight modifications:

,

**Γ C**

*ikk*

results measured for the component chain.

*F*

new powerful method proposed in [20]. A convenient definition for the noise figure of a differential (or multiport) device with respect to one of its ports has been given by Randa

The noise figure in (11) is parameterized by the matrix of reflection coefficients seen by the DUT into the ports of connected components **Γ***k* and the noise correlation matrix of incident noise waves injected by an external source **C***<sup>k</sup>* . **I** is the identity matrix in (11), the dagger indicates the Hermitian conjugate, and **S***k* as well as **C***S a*, are the scattering matrix and the noise correlation matrix of emergent waves contributed by the DUT, respectively. To apply this definition, **C***S a*, has to be determined first. Therefore, the differential device has to be embedded into a network of passive components which provide the differential excitation as only single-ended measurement equipment is currently available. This is demonstrated in Fig. 14. The noise correlation matrix of the DUT then has to be de-embedded from the

**Figure 14.** DUT embedded into passive components. **b***Sx y*, are equivalent generator noise waves

For this purpose, the noise distribution matrix defined in [21] is a convenient starting point. Multiplied by Boltzmann's constant *k* and the physical temperature *T* , it is the correlation matrix of emergent noise waves caused by a passive component which account for all the noise generated within the device. It can be related to the scattering matrix as shown by (12).

caused by component x and ejected from the respective port y.

A short and intuitive proof of this relation is contained in [25]:

 † 1 1 † ,

*k k k k k Sa k k*

*kk k kk kk*

**I S Γ SCS C I S Γ**

**I S Γ SCS I S Γ**

† 1 1 †

*ii*

(11)

*ii*

<sup>3</sup> <sup>1</sup> **S** is a submatrix of **S** .

$$\begin{bmatrix} \mathbf{b}\_{S,2} \\ \vdots \\ \mathbf{b}\_{S,k-1} \\ \mathbf{b}\_{S,k+1} \\ \vdots \\ \mathbf{b}\_{S,n} \\ \mathbf{b}\_{S,d} \end{bmatrix} = \begin{bmatrix} \mathbf{b}\_{S,2} \\ \mathbf{b}\_{S,k+1} \\ \mathbf{b}\_{S,k+1} \\ \vdots \\ \mathbf{V}\_{am} \\ \mathbf{b}\_{S,k} \end{bmatrix} = \begin{bmatrix} \mathbf{V}\_{pm} & \mathbf{V}\_{pp} & \mathbf{V}\_{pa} \\ \mathbf{V}\_{am} & \mathbf{V}\_{ap} & \mathbf{V}\_{am} \end{bmatrix} \begin{bmatrix} \mathbf{b}\_{k-1} \\ \mathbf{b}\_{k-1} \\ \mathbf{b}\_{k+1} \\ \mathbf{b}\_{k+1} \\ \vdots \\ \mathbf{b}\_{n} \\ \mathbf{b}\_{n} \end{bmatrix} \mathbf{b}\_{p} \tag{16}$$

HaLoS – Integrated RF-Hardware Components for Ultra-Wideband Localization and Sensing 393

<sup>ˆ</sup> *m chain kT* **<sup>C</sup>** (21)

**C** (22)

components of the chain related back to the input. For the set-up of Fig. 14, **C***m* is a 1 1

For using (11) in noise figure computations, its parameter matrices *<sup>k</sup>* **Γ** and *Ck* still need to be determined. *<sup>k</sup>* **Γ** contains reflection coefficients, which relate waves injected from the DUT *S a*, *b* to those reflected back from the embedding network *<sup>a</sup> a* . It follows from inspection that *<sup>k</sup>* **<sup>Γ</sup>** is a submatrix of **W**<sup>1</sup> . Focusing on *C<sup>k</sup>* , a simple argument leads to some confidence that (22) is a reasonable choice: Assume that the power splitter at the input of Fig. 14 only excites the differential mode. In this case, noise at the input of the DUT is completely correlated. Also, there should be a noise power of *kT* available at the input of the DUT in differential mode to stay comparable to the standard noise figure definition. Then, due to the properties of mixed-mode transformation, (22) is the evident solution. This

> 0.5 0.5 0 0 0.5 0.5 0 0 0 0 00 0 0 00

*kT kT kT kT* 

Thus, all inputs required for (11) are determined, and the noise figure with respect to a certain output port can be calculated. Instead of a physical port, also a logical port can be considered. For this purpose, matrices in the numerator and the denominator of (11) have to be transformed by an appropriate transformation. In view of Fig. 14, mixed-mode transformation provides noise power spectral densities in the differential mode at the selected output of the DUT for both cases: Noise generated by the DUT and the input sources, as well as noise generated by the input sources alone. Their ratio finally determines the differential noise figure of the device. This approach has been applied to the pseudodifferential amplifier shown in Fig. 15. The result is contained in Fig. 16 together with the noise figure measured from one signal branch, which is given for comparison. In the measurements, the losses of the probe heads have been appropriately taken into account.

The introduction of the feedback-sampling concept by system design spawned the requirement of signal subtraction at the input of the receive path. Hence, the demand for new components equipped with two inputs arose - one for the RF signal taken from the antenna, and another one for a digital prediction signal provided by the signal processing via a digital-to-analog converter (DAC). In theory, subtraction results in an output signal of highly reduced voltage swing to which the analog-to-digital converter (ADC) used for signal acquisition will be exposed. To confirm this theory in practice, two versions of an input subtractor have been implemented and will be presented in the following subsections.

matrix associated with the characteristic noise temperature as shown by (21):

*k*

**3.4. Solutions for the feedback-sampling approach** 

is discussed in [20] in more detail.

In (16), submatrix **V***am* will always be zero, because there is no direct connection from the input to the DUT. Hence, we are left with

$$\mathbf{b}\_{S,p} = \mathbf{V}\_{pm}\mathbf{b}\_m + \left[\mathbf{V}\_{pp} \mid \mathbf{V}\_{pa}\right] \begin{bmatrix} \mathbf{b}\_p\\ \mathbf{b}\_a \end{bmatrix} \tag{17}$$

and

$$\mathbf{b}\_{S,a} = \left[\mathbf{V}\_{ap} \mid \mathbf{V}\_{aa}\right] \begin{bmatrix} \mathbf{b}\_p\\ \mathbf{b}\_a \end{bmatrix}. \tag{18}$$

Setting 1 | | *ap aa pp pa* **Q VV VV** for abbreviation, (19) is obtained from (17) and (18) after some algebra4:

$$\mathbf{Q}\,\mathbf{V}\_{pm}\,\mathbf{b}\_{m}=\mathbf{Q}\,\mathbf{b}\_{S,p}-\mathbf{b}\_{S,a}\,.\tag{19}$$

Finally, since *S p*, **b** and *S a*, **b** arise from different sources and are thus uncorrelated, **C***S a*, can be determined from (20)

$$\begin{aligned} \mathbf{Q} \mathbf{V}\_{pm} \mathbf{C}\_m \mathbf{V}\_{pm}^\dagger \mathbf{Q}^\dagger &= \mathbf{Q} \mathbf{C}\_{S,p} \mathbf{Q}^\dagger + \mathbf{C}\_{S,\mu} \\\\ \text{with } \mathbf{C}\_m = \overline{\mathbf{b}\_m \mathbf{b}\_m^\dagger}, \quad \mathbf{C}\_{S,p} = \overline{\mathbf{b}\_{S,p} \mathbf{b}\_{S,p}^\dagger}, \quad \text{and } \mathbf{C}\_{S,\mu} = \overline{\mathbf{b}\_{S,\mu} \mathbf{b}\_{S,\mu}^\dagger}. \end{aligned} \tag{20}$$

In (20), noise correlation matrices of single passive components given by the product of *kT* and (12) are composed to the block diagonal matrix5 **C***S p*, . **C***m* accounts for noise from all

<sup>4</sup> As the right division function of a math program can be used to compute **Q** , there is no need for an explicit inversion, and a minimum norm solution is obtained for a non-square system.

<sup>5</sup> Note that noise contributions of the output loads, according to [22], should not be considered for NF computation. With respect to the set-up of Fig. 14 this implies ! ,5,1 ,5,1 0 *S S b b* , which can be achieved by using the second stage correction of the NF meter.

components of the chain related back to the input. For the set-up of Fig. 14, **C***m* is a 1 1 matrix associated with the characteristic noise temperature as shown by (21):

392 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications

,2

, 1

*S k*

,

*S n*

1

inversion, and a minimum norm solution is obtained for a non-square system.

With respect to the set-up of Fig. 14 this implies

correction of the NF meter.

**b**

, ,

*S a S k*

input to the DUT. Hence, we are left with


and

Setting

some algebra4:

be determined from (20)

*S p S k*

**b**

<sup>1</sup> , , 1

**V VV <sup>b</sup> <sup>b</sup> <sup>b</sup>**

**<sup>b</sup> <sup>b</sup> <sup>b</sup> <sup>b</sup>**

In (16), submatrix **V***am* will always be zero, because there is no direct connection from the

, <sup>|</sup>*<sup>p</sup> S p pm m pp pa*

> , <sup>|</sup>*<sup>p</sup> S a ap aa*

Finally, since *S p*, **b** and *S a*, **b** arise from different sources and are thus uncorrelated, **C***S a*, can

with , , and .

In (20), noise correlation matrices of single passive components given by the product of *kT* and (12) are composed to the block diagonal matrix5 **C***S p*, . **C***m* accounts for noise from all

4 As the right division function of a math program can be used to compute **Q** , there is no need for an explicit

5 Note that noise contributions of the output loads, according to [22], should not be considered for NF computation.

!

**QV C V Q QC Q C**

**C bb C b b C b b**

†† †

*m m m Sp Sp Sp Sa Sa Sa*

*pm m pm Sp Sa*

†† † , ,, , ,,

, ,

**Q VV VV** for abbreviation, (19) is obtained from (17) and (18) after

**b Vb V V**

**b VV**

*<sup>m</sup> <sup>S</sup>*

**<sup>b</sup> <sup>b</sup> <sup>b</sup>**

*pm pp pa k*

*am ap aa k p*

**V VV b b**

1

2

**b**

1

(16)

**<sup>b</sup>** , (17)

**<sup>b</sup>** . (18)

(20)

*n*

**b**

*a*

**b**

*a*

**b**

*k a*

, , *pm m Sp Sa* **QV b Qb b** . (19)

,5,1 ,5,1 0 *S S b b* , which can be achieved by using the second stage

$$\mathbf{C}\_m \approx \left[ k \, \hat{T}\_{chain} \right] \tag{21}$$

For using (11) in noise figure computations, its parameter matrices *<sup>k</sup>* **Γ** and *Ck* still need to be determined. *<sup>k</sup>* **Γ** contains reflection coefficients, which relate waves injected from the DUT *S a*, *b* to those reflected back from the embedding network *<sup>a</sup> a* . It follows from inspection that *<sup>k</sup>* **<sup>Γ</sup>** is a submatrix of **W**<sup>1</sup> . Focusing on *C<sup>k</sup>* , a simple argument leads to some confidence that (22) is a reasonable choice: Assume that the power splitter at the input of Fig. 14 only excites the differential mode. In this case, noise at the input of the DUT is completely correlated. Also, there should be a noise power of *kT* available at the input of the DUT in differential mode to stay comparable to the standard noise figure definition. Then, due to the properties of mixed-mode transformation, (22) is the evident solution. This is discussed in [20] in more detail.

$$\mathbf{C}\_{k} = \begin{bmatrix} 0.5kT & -0.5kT & 0 & 0 \\ -0.5kT & 0.5kT & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{bmatrix} \tag{22}$$

Thus, all inputs required for (11) are determined, and the noise figure with respect to a certain output port can be calculated. Instead of a physical port, also a logical port can be considered. For this purpose, matrices in the numerator and the denominator of (11) have to be transformed by an appropriate transformation. In view of Fig. 14, mixed-mode transformation provides noise power spectral densities in the differential mode at the selected output of the DUT for both cases: Noise generated by the DUT and the input sources, as well as noise generated by the input sources alone. Their ratio finally determines the differential noise figure of the device. This approach has been applied to the pseudodifferential amplifier shown in Fig. 15. The result is contained in Fig. 16 together with the noise figure measured from one signal branch, which is given for comparison. In the measurements, the losses of the probe heads have been appropriately taken into account.

### **3.4. Solutions for the feedback-sampling approach**

The introduction of the feedback-sampling concept by system design spawned the requirement of signal subtraction at the input of the receive path. Hence, the demand for new components equipped with two inputs arose - one for the RF signal taken from the antenna, and another one for a digital prediction signal provided by the signal processing via a digital-to-analog converter (DAC). In theory, subtraction results in an output signal of highly reduced voltage swing to which the analog-to-digital converter (ADC) used for signal acquisition will be exposed. To confirm this theory in practice, two versions of an input subtractor have been implemented and will be presented in the following subsections.

### *3.4.1. Pseudo-differential feedback-sampling amplifier*

Similar to the design of amplifiers for the basic system, the development of the feedbacksampling amplifier has been guided by the assumption that the receive signal in the RF path is rather week and sufficient amplification has to be provided, while the least amount of excess noise should be added. Hence, the amplifier of Fig. 12 has been reviewed and was deemed to be suited as RF input stage of the new topology. In Fig. 15, it can be identified in the dashed box on the left-hand side. Some adjustments - especially with respect to the values of components in the feedback network - had to be made, though, as the application required a shift in the covered frequency range. At that time, the prediction signal had to be provided by a current steering DAC and can be assumed to be of rather large signal swing. Hence, no amplification is provided for this signal. Promoted by the nature of the prediction signal, the required signal subtraction is performed in the current domain. In Fig. 15, two current mirrors inject their output signals into a common output node for this purpose. While this implies signal addition instead of signal subtraction at first glance, signal addition can be turned into signal subtraction by simple sign inversion, which is enabled either by exploiting the properties of the pseudo-differential amplifier structure itself or by sign selection of the prediction signal in the digital domain. The special current-mirror arrangement of Fig. 15 has been chosen for balancing the maximum output powers which is important to ensure that the signal from the DAC input can cancel the signal from the RF input. Linearity of both signal paths, transconductance from the DAC input to the common output and maximum output currents of the DAC have to be harmonized to account for this requirement.

HaLoS – Integrated RF-Hardware Components for Ultra-Wideband Localization and Sensing 395

**Figure 16.** Measurement results for the RF path of the feedback-sampling amplifier. (The arrows point

0.0 Hz 1.0 GHz 2.0 GHz 3.0 GHz 4.0 GHz 5.0 GHz

frequency

2.0

3.0

4.0

5.0

6.0

7.0

8.0

This topology has been characterized in detail. Results for the RF signal path are presented

As explained for the pseudo-differential amplifier in section 3.2.3, the PM 8 probe station equipped with GSSG-probes can be used to examine an individual differential signal path. In order to detect the mixed-mode parameters given in Fig. 16, the device has been exposed to true mode excitation provided by the network analyzer, while calibration data have been applied to compensate for losses caused by the test set-up. Noise characterization can be performed by the method presented in section 3.3 and has been discussed in [19][20]. A remarkable feature of the results of this measurement is the fact that the differential noise figure *NFdiff* does not coincide with the noise figure measured from one signal path6 *NFSE* . Especially at higher frequencies, a large deviation occurs. In [20], this is explained by crosstalk caused by parasitics. So, the use of differential de-embedding schemes is recommended instead of a single-ended noise figure measurement from one signal branch. However, in view of the aim to assess the capabilities of the feedback-sampling approach, the signal subtraction itself is most interesting. In [27], we presented different test set-ups for verification purposes. Fig. 17 shows four representative results which confirm the ability to

6 In Fig. 16, NF curve progressions start at 1 GHz because this is the lower corner frequency of the hybrid couplers

cancel the RF signal by an appropriate prediction signal.

to the related axis scaling.)



0

10

20

30

in Fig. 16.

used for measurement.

**Figure 15.** Half-circuit schematic diagram (left) and chip photograph (right) of the feedback-sampling LNA

394 Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications

Similar to the design of amplifiers for the basic system, the development of the feedbacksampling amplifier has been guided by the assumption that the receive signal in the RF path is rather week and sufficient amplification has to be provided, while the least amount of excess noise should be added. Hence, the amplifier of Fig. 12 has been reviewed and was deemed to be suited as RF input stage of the new topology. In Fig. 15, it can be identified in the dashed box on the left-hand side. Some adjustments - especially with respect to the values of components in the feedback network - had to be made, though, as the application required a shift in the covered frequency range. At that time, the prediction signal had to be provided by a current steering DAC and can be assumed to be of rather large signal swing. Hence, no amplification is provided for this signal. Promoted by the nature of the prediction signal, the required signal subtraction is performed in the current domain. In Fig. 15, two current mirrors inject their output signals into a common output node for this purpose. While this implies signal addition instead of signal subtraction at first glance, signal addition can be turned into signal subtraction by simple sign inversion, which is enabled either by exploiting the properties of the pseudo-differential amplifier structure itself or by sign selection of the prediction signal in the digital domain. The special current-mirror arrangement of Fig. 15 has been chosen for balancing the maximum output powers which is important to ensure that the signal from the DAC input can cancel the signal from the RF input. Linearity of both signal paths, transconductance from the DAC input to the common output and maximum output currents of the DAC have to be harmonized to account for this

**Figure 15.** Half-circuit schematic diagram (left) and chip photograph (right) of the feedback-sampling

*3.4.1. Pseudo-differential feedback-sampling amplifier* 

requirement.

LNA

**Figure 16.** Measurement results for the RF path of the feedback-sampling amplifier. (The arrows point to the related axis scaling.)

This topology has been characterized in detail. Results for the RF signal path are presented in Fig. 16.

As explained for the pseudo-differential amplifier in section 3.2.3, the PM 8 probe station equipped with GSSG-probes can be used to examine an individual differential signal path. In order to detect the mixed-mode parameters given in Fig. 16, the device has been exposed to true mode excitation provided by the network analyzer, while calibration data have been applied to compensate for losses caused by the test set-up. Noise characterization can be performed by the method presented in section 3.3 and has been discussed in [19][20]. A remarkable feature of the results of this measurement is the fact that the differential noise figure *NFdiff* does not coincide with the noise figure measured from one signal path6 *NFSE* . Especially at higher frequencies, a large deviation occurs. In [20], this is explained by crosstalk caused by parasitics. So, the use of differential de-embedding schemes is recommended instead of a single-ended noise figure measurement from one signal branch. However, in view of the aim to assess the capabilities of the feedback-sampling approach, the signal subtraction itself is most interesting. In [27], we presented different test set-ups for verification purposes. Fig. 17 shows four representative results which confirm the ability to cancel the RF signal by an appropriate prediction signal.

<sup>6</sup> In Fig. 16, NF curve progressions start at 1 GHz because this is the lower corner frequency of the hybrid couplers used for measurement.

Those measurements were obtained from a test set-up incorporating the PM 8 probe station with GSSG-probes, in which two signal generators7 synchronized by a frequency standard provided the input signals to both inputs at appropriate power levels via two hybrid couplers. The differential output signal of the DUT was recombined by a third hybrid coupler and displayed by a signal analyzer8. In Fig. 17, no loss compensation is applied and results are clipped to 100 kHz span. Two cases can be distinguished: First, the digital prediction signal has been switched off (DAC*off*) and only the RF signal has been present at the inputs. Then, also the prediction signal has been applied (DAC*on*) and a notable reduction in output signal power can be observed for all frequencies.

HaLoS – Integrated RF-Hardware Components for Ultra-Wideband Localization and Sensing 397

A printed circuit board has been designed to enable joint performance evaluation of this amplifier and the 7 Ω antenna. Due to the low feeding point impedance, separate characterization is less useful. To avoid problems involved in interconnecting devices with 7 Ω reference impedance, the amplifier should directly be attached to the antenna, which is supported by the board. Thus, both evaluation and refinement of this circuit will have to be

The circuits introduced in this section serve for the M-sequence topology. They have been implemented in a cost-efficient 0.25 µm Silicon Germanium BiCMOS technology, which opens up new fields of ultra-wideband radar applications. In the following sub-chapters, the design of different hardware blocks for the ultra-wideband radar front-end is presented. The design of a multi-purpose M-Sequence generator is presented which acts as a pulse compression modulator and exhibits an up-conversion mixer. A highly efficient powerdistributed amplifier has been implemented utilizing a novel cascode power matching

**Figure 18.** Schematic diagram (left) and chip photo (right) of the subtractor.

**4. Transmitter circuits** 

**4.1. Introduction** 

performed in close collaboration with our partners from the *ultraMedis* project.

the DAC. In this implementation, noise figure is traded against linearity, as input signals close to 0 dBm might occur. For its implementation, component parameters have been determined by a semi-automated procedure, in which the input stage - a common base configuration - was optimized with respect to input power matching, while an upper bound for *NFmin* was respected and noise matching was clearly observed. As in the case of the feedback-sampling amplifier according to Fig. 15, signal subtraction is performed in the

current domain using a common output node.

**Figure 17.** Signal subtraction enabled by the feedback-sampling amplifier.

### *3.4.2. Subtractor with Low Impedance antenna interface*

The feedback-sampling amplifier of the preceding subsection is expected to perform well as long as the assumption of (reasonable) small input signals is justified. A key requirement in the feedback-sampling concept is linearity preceding the signal subtraction in order not to distort the zero crossings which are sampled by the analog-to-digital converter. However, as soon as array operation is considered, antenna cross-talk is likely to violate this assumption. In addition, a dense antenna array requires the antennas to have small outer dimensions. This can be achieved by dielectrically scaling the antennas, which - in turn - leads to a low (7 Ω) feeding point impedance. The latter has to be interfaced by the subtraction circuit. The topology shown in Fig. 18 is a first approach towards an analog subtractor which provides appropriate single-ended inputs to interface with both, a dielectrically scaled antenna and

<sup>7</sup> Rhode & Schwarz SMJ100A

<sup>8</sup> Rhode & Schwarz FSV

the DAC. In this implementation, noise figure is traded against linearity, as input signals close to 0 dBm might occur. For its implementation, component parameters have been determined by a semi-automated procedure, in which the input stage - a common base configuration - was optimized with respect to input power matching, while an upper bound for *NFmin* was respected and noise matching was clearly observed. As in the case of the feedback-sampling amplifier according to Fig. 15, signal subtraction is performed in the current domain using a common output node.

**Figure 18.** Schematic diagram (left) and chip photo (right) of the subtractor.

A printed circuit board has been designed to enable joint performance evaluation of this amplifier and the 7 Ω antenna. Due to the low feeding point impedance, separate characterization is less useful. To avoid problems involved in interconnecting devices with 7 Ω reference impedance, the amplifier should directly be attached to the antenna, which is supported by the board. Thus, both evaluation and refinement of this circuit will have to be performed in close collaboration with our partners from the *ultraMedis* project.
