CHAPTER 1 Introduction
1.2 Thesis Organization
In Chapter 2, the factors degrading EVM are identified and introduced how they influence EVM. And EVM specification of WiMAX is also defined.
In Chapter 3, the I/Q modulator with compensating I/Q imbalance match and LO feedthrough is designed. Also the compensation algorithm is proposed to cooperate with the I/Q modulator.
In Chapter 4, the circuit implement and measurement results are presented.
In the last Chapter, the work is summarized and concluded.
CHAPTER 2
EVM in Direct-Conversion Transmitter Consideration
2.1 Direct-Conversion Transmitter
The direct-conversion transmitter combines the signals of I and Q channels and converts baseband signals to radio-frequency. First the baseband codes are translated to analog signals by D/A converters and low-pass filters to suppress out-band spurious noise. Then the signals of I and Q channels are up-converted to RF and combined together by I/Q modulator. Almost over 90% of transmitter gain is in the RF block from the I/Q modulator to the PA. An RF band-pass filter is inserted between the driver amplifier and the PA to suppress the out-of-band interference.
Fig 2.1 Block diagram of direct-conversion transmitter
The signal level in the transmitter is normally much higher than that in a receiver, and thus the noise figure is not as critical in the transmitter as in the receiver. The important parameters for a transmitter are the output power, especially the maximum output power, and the fidelity of the transmission waveform measured by modulation accuracy, EVM. In addition to these parameters of the desired transmission signal, the unwanted emissions, such as adjacent channel power and in-band and out-band noise/spurs emissions, are usually well defined in the mobile transmitter specifications.
This Chapter focuses on EVM analysis of direct-conversion transmitter. The sources that degrading EVM are discussed below.
2.2 Sources of Degrading EVM in General Consideration
EVM may be degraded by Intersymbol or Interchip Interference (ISI or ICI), Close-in phase noise of synthesized LO, LO feedthrough, I/Q Imbalance, and Nonlinearity. These sources are induced by the circuit blocks in direct-conversion transmitter and indicated in Fig. 2.2. We can identify how they affect EVM by [1]-[3]
and define the system requirements to meet the specification.
Fig 2.2 Factors degrading EVM in direct-conversion transmitter.
2.2.1 Intersymbol or Interchip Interference (ISI or ICI)
Intersymbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have similar effect as noise, thus making the communication less reliable. ISI is usually caused by multipath propagation and the inherent non-linear frequency response of a channel. Ways to fight against intersymbol interference include adaptive equalization and error correcting codes.
The ISI or ICI of symbols or chips may have been created at beginning to generate a transmission signal. To obtain high spectral efficiency of the transmission
signal, the originally rectangular symbol or chip waveform is reshaped, and it is also called pulse shaping. The shaped symbol (or chip) waveform aTX_ideal can be expressed as
_ ( )
TX ideal PS rect
a =h ∗a t . (2-1) In the wireless systems, a complementary filter with an impulse response hPS_C is normally used in the corresponding receiver side to equalize the phase and magnitude distortion and thus to eliminate or to minimize the ISI or ICI caused by the pulse shaping in the transmitter.
The filters in the transmitter path other than the pulse-shaping filter may cause the degradation of the modulation accuracy degradation especially when the pass-band of the filter, such as a channel filter, is close to the bandwidth of the transmission signal. Assuming the impulse response of the filter is hfltr(t), the shaped symbol or chip waveform aTX_ideal after passing through the filter turns into
( ) ( ) _ ( )
TX fltr TX ideal
a t =h t ∗a t . (2-2) The corresponding EVMISI can be expressed by the impulse response function as [4]
2
The terms in the numerator in the square root of (2-3) right side are ISIs or ICIs to the symbol or chip at t0, and they are contributed from adjacent and other symbols or chips. Each term in the square root of (2-3) can be also obtained by means of the following formula:
0
where k is equal to 1,2,3,…, and 2δt is the duration of sampling pulse. The equation (2-3) could be written as
2 ( )
ISI ICI
EVM ∞ I k
−∞
=
∑
Δ . (2-5)2.2.2 Close-in Phase Noise of Synthesized LO
Another main contribution to the degradation of the modulation accuracy is the close-in phase noise of the synthesizer applied as local oscillator of the up-converter in the transmitter. Assuming the vector error caused by the synthesizer phase noise
n(t) can be expressed as
'( ) ( ) ( ) ( ) exp( n( )) a tG =a tG +e tG =a tG jφ t
. (2-6) The magnitude of the vector error then can be expressed as
2 2 2
( ) '( ) ( ) n e t = a t −a t ≅φ
G G G
, (2-7) where |a(t)| is normalize to 1. The statistical average of n2(t) is the autocorrelation function of the phase noise. The autocorrelation function and the power spectrum density Sn(f) have the following relationship
/ 2
{ }
Hence the EVMNphase resulting from the phase noise of the synthesizers could be written as
Nphase Nphase
EVM = P . (2-9) Usually the phase noise within the loop bandwidth of synthesizers used in the mobile transmitters is in the range of -60 to -80 dBc/Hz. In the case of the synthesizer loop bandwidth being reasonable wide, PNphase could be approximated as
/10
2 10Nphase _
Nphase synth loop
P ≅ ⋅ ⋅BW , (2-10) Where Nphase is the average phase noise, in dBc/Hz, within the synthesizer loop bandwidth, and BWsynth_loop is the bandwidth of the synthesizer loop filter in Hz. The EVMNphase in (2-4) could be modified as
/10
2 10Nphase _
Nphase Nphase synth loop
EVM = P ≅ ⋅ BW (2-11) The equation if (2.11) could help us to define the specification of phase noise and loop bandwidth in the system.
2.2.3 LO Feedthrough
The DC offset in the baseband I and Q channels will cause LO feedthrough, and it will degrade the modulation accuracy of the transmission signal. Assuming the dc offset in the baseband I and Q channels are ∆Idc and ∆Qdc. The baseband signal a’I(t) and a’Q(t), in the I and Q channels are respectively represented by
' ( ) cos ( )I dc
a t = φ t + Δ (2-12) I ' ( ) sin ( )Q dc
a t = φ t + ΔQ . (2-13) At the output of the modulator, the I and Q quadrature signals turn into a signal with an RF carrier, and it can be expressed as
[ ]
2 2
The modulated signal is shown in Fig. 2.3 and also LO feedthrough induced error vector are indicated. How LO feedthrough affecting signal constellation could clearly be found out that it also contributes an error vector.
Fig. 2.3 LO feedthrough induced error vector
Since I/Q axis of I/Q constellation is moved by the LO feedthrough term of (2-14), from Fig2.3, the <e(t)> is with the same magnitude of ∆dc and reverse direction of ∆θ. LO feedthrough suppression (LOFTS) in dB could be defined as
10log 20log 20log
, where VLOFT is ∆dc and VTX is A(t). And then EVMLOFT which is contributed by LO feedthrough could simply be written as
( ) 20
So, the equation (2.20) could help us to define system specification of EVM which is degraded by LO feedthrough.
2.2.4 I/Q Imbalance
For single sideband modulation the amplitude and phase mismatches between I and Q generate unwanted sideband signal. By using ε and σ to represent amplitude and phase mismatches between quadrature LO signals, respectively. At the output of the modulator, the I and Q quadrature signals turn into a signal with an RF carrier, and it can be expressed as
[ ]
The upper side of (2-21) is the desired signal and the lower side of (2-22) is the unwanted sideband signal. Hence the sideband suppression (SBS) in dB could be calculated as2
Fig 2.4 Unwanted sideband signal induced error vector
After received by the receiver, the transmitter output is converted to baseband I and Q channels as
, where β is (γ-δ). The received signal constellation could be affected by the unwanted sideband signals as Fig.2.4 shown. When β is equal to zero, EVMSB which is contributed by unwanted sideband is on the worst degradation and could be written as
1020
So, the equation (2-27) could help us to define system specification of EVM which is degraded by I/Q imbalance.
2.2.5 Nonlinearity Influence
Transmitter usually operates well below its 1-dB compression point (P-1dB). Thus, among the nonlinear effects, the third-order intermodulation of two nearby interferers is the major EVM contributor. The input third order intermodulation interception point is in-band interference power of the 3rd intermodulation product. Hence the interference power could be written as
3 inf 2 inf 2 3 3 inf 2 3
IM o i o
P =P + P − IIP = P − OIP , (2-29) where OIP3 is the output 3rd intercept point.
The EVM caused by 3rd intermodulation is just the square root ratio of the PIM3 to the desired RF signal power (PRFO), as following
3 3 inf 2 3
And it could be used to define the system specification.
Since the nonlinearity in the transmitter is dominated by power amplifier (PA), the distortion of PA contains the amplitude distortion (AM-AM) and phase distortion (AM-PM). And the equation (2-30) just describes the intermodulation influence.
Furthermore the EVM degraded by PA is defined clearly in [4].
2.2.6 Total EVM
If all factors contributing to the degradation of the modulation accuracy are uncorrelated, the overall EVM if the transmission signal can be expressed as
2
2 2 2 2 2
3
total k
k
ISI Nphase CFT SB IM
EVM EVM
EVM EVM EVM EVM EVM
=
= + + + +
∑
(2-31)2.3 EVM in WiFi and WiMAX
EVM requirements for 802.11 are specified at -25 dB, which is required to achieve a 10% packet error rate. For 802.16, EVM is held to -31 dB, which is based on a 1% packet error rate. This lower error rate helps contribute to WiMAX longer range. The difference between 802.16 and 802.11 is indicated in TABLE I.
TABLE I Difference between 802.11 and 802.16
WLAN (802.11) WiMAX (802.16) Bandwidth Fixed; 20 MHz/52
Subcarriers Variable; 1 to 28MHz/256 Subcarriers
Guard Interval Fixed at 1/4 * Symbol Time
Variable; Ranges from 1/32 to 1/4 * Symbol Time Spectral Efficiency 2.7 Mbits/s/Hz 3.1 to 3.8 Mbits/s/Hz
EVM Requirements -25 dB -30 dB
Receive Noise Figure 10 dB Maximum 7 dB Maximum
Duplexing TDD TDD, FDD, HFDD
Spectrum Unlicensed Licensed & Unlicensed Transmit Dynamic Range Tx Power Fixed 50-dB Range
A proper specification of sources degraded EVM are defined in Table I from [5]
[6]. Since the EVM specification of 802.16 is stricter than 802.11, the RF transmitter of WiMAX could meet the requirement of WiFi by shifting carrier frequency.
From Fig. 2.2, the I/Q modulator includes two factors of degrading EVM, such as LO feedthrough and I/Q imbalance. So, in this work, I/Q modulator with eliminating LO feedthrough and I/Q imbalance are designed.
TABLE II EVM contribution from each source
Source EVM (%) EVM (dB)
ISI/ICI 0.5 -46
LO Phase Noise 2.37 -32.5
Carrier Feedthrough 0.56 -45
I/Q imbalance 1.58 -36
Nonlinearity 1 -40
Total 3.11 -30.13
2.4 Summary
The factors degrading EVM has been identified. We can realize how they degrading EVM by some circuit characteristics, such as ISI or ICI rising after passing channel filters, phase noise of synthesizer, unwanted sideband suppression, LO feedthrough suppression, and the input third order intermodulation interception point.
The specification about EVM in WiMAX is -30dB. From the circuit characteristics mentioned before, a proper specification for the factors degrading EVM and the required circuit characteristics is defined.
CHAPTER 3
Circuit Design for Direct Up-Conversion Mixer with Matching Compensation Eliminating I/Q Imbalance and LO Feedthrough in WiMAX and WiFi
Transmitter
The auto-compensation techniques for I/Q imbalance can be separated into two kinds of feedback loops of power detection loop [7] and dummy path for extracting error messages [8]. The power detection loop needs more iteration for achieving an optimal condition and less additional hardware. The loop with dummy path for extracting error messages can get error messages with less iteration but needs more hardware.
However, the two feedback loops need an open loop circuit to tune the I/Q magnitude imbalance and phase imbalance. In this work, I/Q modulator with an open loop compensation circuit to tune the I/Q imbalance and LO feedthrough is presented.
Since LO buffers are originally needed, we design the LO buffers with magnitude and phase tuning without another hardware. An auto-compensation algorithm is developed for power detection loop with advantage of needing less additional hardware. By applying the algorithm for co-simulated with the I/Q modulator, the specification of EVM in Table II can be achieved.
The proposed I/Q modulator in this thesis is shown in Fig. 3.1. The I/Q mixer is based on conventional double balanced Gilbert Cell mixer with LO feedthrough
adjustments. Before LO I/Q signals is fed the I/Q mixer, LO buffers are placed to tune the magnitude and phase of LO I/Q signals. The two stages of polyphase filter are placed before I/Q buffer to generate quadrature LO signals for measurement consideration.
Fig. 3.1 Proposed I/Q modulator
3.1 LO Feedthrough in Up-Conversion Mixer Consideration
The main advantage of double balanced Gilbert Cell mixer shown in Fig. 3.2 is LO cancellation. However, LO feedthrough accompanies imperfect LO cancellation.
The LO feedthrough due to dc current offset induced by the transconductance stages (Mt+ and Mt-) device mismatch, switching stage device mismatch, and differential LO signals imbalance, are identified in this thesis. A compensation method is developed to suppress the LO feedthrough.
3.1.1 Factors of Inducing LO Feedthrough
First, we need to identify whether the switching stage (MS1-MS4) or the transconductance stages (Mt+ and Mt-) device mismatch of a double balanced Gilbert Cell mixer causes a larger LO feedthrough. The switching stage (MS1-MS4) device mismatch induces the DC current mismatch of MS1 and MS3 or MS2 and MS4. This DC current mismatch causes imperfect LO cancellation. However, it has less impact to LO feedthrough since the double balanced mixer uses differential topology and can suppress it. The DC current offset between the transconductance stages, Mt+, and Mt-, is induced by the transconductance stages (Mt+, Mt-) device mismatch. If the DC current of Mt+ is larger than Mt-, it should further degrade the current matching of MS1
and MS3, or MS2 and MS4. This effect can’t just be suppressed by differential topology.
Here, the Monte-Carlo simulations of LO feedthrough use Table III which is supported in TSMC 0.18um technical documents for device mismatch reference. As Fig. 3.3 and Fig. 3.4, the switching stage (MS1-MS4) device mismatch induces small LO feedthrough and the two transconductance stages (Mt+, Mt-) device mismatch induces larger one. So, the main factor degrading LO feedthrough is the transconductance stages (Mt+, Mt-) device mismatch. So, the DC current offset of the
Table III TSMC 0.18um technical documents for device mismatch reference
1.8V NMOS 1.8V PMOS 3.3V NMOS 3.3V PMOS
σVth0 (mV) 3.635*geo_fac 4.432* geo_fac 6.227* geo_fac 4.525* geo_fac σXL / L (%) 0.458* geo_fac 0.396* geo_fac 0.365* geo_fac 0.247* geo_fac σXW / W (%) 0.373* geo_fac 0.326* geo_fac 0.298* geo_fac 0.201* geo_fac σTox / Tox (%) 0.101* geo_fac 0.0873* geo_fac 0.0804* geo_fac 0.0543* geo_fac
Where geo_fac=1/sqrt(N*Leff*Weff) (1/um)
two transconductancestages needs to be compensated.
Besides DC current offset, there is another factor degrading LO feedthrough, the differential LO signals imbalance. The differential LO signals imbalance can be viewed as a common mode signal existing in differential LO signals. Since the source couple pair is with high common mode rejection ratio, the LO cancellation could be almost perfect. However, the differential LO signals imbalance could still enlarge LO feedthrough when the MS1-MS4 or the two transconductancestages (Mt+, Mt-) are with device mismatch. If the DC current offset of the two transconductancestages can be compensated, the differential LO signals imbalance can be ignored.
Fig. 3.2 Double balanced Gilbert Cell mixer
20 40 60 80 100 120 140 160 180
Fig. 3.3 Monte-Carlo analysis of LO feedthrough due to switching stage device mismatch
Fig. 3.4 Monte-Carlo analysis of LO feedthrough due to switching stage and transconductance stage device mismatch
3.1.2 I/Q Mixer Design for LO Feedthrough Suppression
Gilbert cell is used for I/Q mixer topology with resonant loads of LC tanks and current summation for combining I-channel and Q-channel signals as shown in Fig.3.7. The I/Q mixer is designed with IIP3 of 10dBm and conversion gain of -7dB at LO power of 6dBm. The total power consumption of I/Q mixer is 13.8mW.
The DC current offset resulting from device mismatch of the two transconductance stages needs to be suppressed to lower LO feedthrough. A compensating circuit with IDACs has applied to compensate DC current offset of the two transconductance stages in the I/Q mixer, as shown in Fig.3.7. The two switches of MIS+ and MIS- or MQS+ and MQS- decide which transconductance stage of MIt+ and MIt- or MQt+ and MQt- has less current and needs to be compensated. Since the IDACs have quantization error, the compensation of DC current offset is imperfect. The optimal resolution of the IDACs needs to be identified and ensures the quantization error of it doesn’t degrade LO feedthrough too much.
The I/Q mixer is designed with output signal of 0dBm, since it has good linearity.
From Table II, LO feedthrough needs 45dB suppression relating to desired signal.
Since the desired signal power of the I/Q mixer in this work is 0dBm, the LO feedthrough needs to be designed below -45dBm. By using the standard deviation of device mismatch in Table III for Monte-Carlo analysis, the maximum allowed DC current offset between the two transconductance stages can be identified. From the result shown in Fig.3.5, the DC current offset between the two transconductance stages needs to be set below 5uA to obtain LO feedthrough of -45dBm. On the other hand, the quantization error and the resolution of the IDAC have a maximum value of 5uA and 10uA. Besides, the maximum DC current offset of the two transconductance stages can be obtained by Monte-Carlo analysis of the two transconductance stages device mismatch. As the result of Fig.3.6 shown, the maximum DC current offset is 80uA. Two 4-bit IDACs are used to provide the compensation current with 0~150uA to cover the maximum DC current offset and each bit resolution is 10uA in the I/Q mixer.
However, in practice the routing difference of double balanced mixer induces
imperfect LO cancellation, and LO feedthrough is generated. An inverse phase of LO feedthrough can be induced by using IDACs and then compensate it.
Since the DC current offset is with the order of 10-6 ampere, it’s hardly to sense the current difference between the two transconductance stages. In this work, a compensation algorithm is used to directly detect the power of LO feedthrough and find the optimal compensation current with minimum power of LO feedthrough. This algorithm is discussed in session 3.4.1.
20 40 60 80 100 120 140 160 180
Fig. 3.5 Monte-Carlo analysis of LO feedthrough due to switching stage device mismatch with the DC current offset of the two transconductance stages 5uA
20 40 60 80 100 120 140 160 180
Fig. 3.6 DC current offset of the two transconductance stages device mismatch by Monte-Carlo analysis
Fig. 3.7 Proposed I/Q mixer
3.2 I/Q Imbalance Compensation Circuit Design for Up-Conversion I/Q Mixer
3.2.1 I/Q Imbalance Equivalent Model
In homodyne system, the up-converter is composed of I/Q mixer, I/Q LO, and summation circuit. Both imbalance I/Q baseband signals and imbalance I/Q LO signals bring magnitude and phase mismatches to the I/Q modulator. The mismatch model of I/Q modulator is shown as Fig.3.8. After some calculations, all the non-ideal effects due to both baseband and LO signals can be all refer to LO only, as indicated in Fig.3.8. So by adjusting the magnitude of LO Q-path and phase of LO I-path, we can compensate I/Q imbalance.
1 LO 1
Fig. 3.8 I/Q imbalance equivalent model
3.2.2 I/Q Imbalance Compensation Mechanism
I/Q mismatch could be compensated by adding some vector on I or Q path. A simple I/Q constellation of QPSK is shown in Fig.3.9(a). In this work, both the magnitude and phase mismatch will be manipulated using magnitude compensation.
Fig. 3.9 (a) The constellation of QPSK and the error vector. (b) The error vector analysis in I/Q plane
For example, from Fig.3.9(b) the I-channel signal accrue with non-quadrature phase error relating to Q-channel. This phase error is mainly generated by <eQ> and could be taken away by tacking on some Q-channel signal which is with equal magnitude of
<eQ> and in reverse direction of <eQ>. An error vector <e1> can be referred to I-axis and it can be thought as I channel signal induces magnitude error onto Q channel. If
<eQ> and in reverse direction of <eQ>. An error vector <e1> can be referred to I-axis and it can be thought as I channel signal induces magnitude error onto Q channel. If